Spectral Feature-Encoded PINNs for Solving High-Frequency Dynamic Differential Equations

Solving high-frequency differential equations in dynamics is a critical yet challenging task in engineering. Although physics-informed neural networks (PINNs) have shown promise in solving differential equations, their practical application is limited by the spectral bias issue that makes them struggle to capture high-frequency oscillatory patterns. To overcome this limitation, this study proposes the spectral feature-encoded physics-informed neural network (SFE-PINN). By explicitly incorporating the spectral characteristics of differential equations into the neural network architecture, SFE-PINN significantly enhances the modeling of multi-scale oscillatory systems. The core innovation lies in a feature-encoded layer derived from the analytical solution structure of constant-coefficient differential equations. This layer transforms the input variables into a spectral space, effectively decoupling high-frequency dynamics and reducing the complexity of nonlinear fitting. Numerical experiments demonstrate that SFE-PINN outperforms existing algorithms in solving high-frequency ordinary differential equations and shows advantages in solving high-frequency spatiotemporal coupled partial differential equations by combining separation of variables with spectral decoupling strategies. This advancement highlights the potential of SFE-PINN for practical engineering applications, such as large-scale structural dynamic response analysis and elastic wave propagation modeling, where high-frequency phenomena are prevalent.